Tevatron Top Afb Versus LHC Top Physics

Abstract

We carry out a comprehensive analysis of models for top AFB at CDF in light of new top data arriving from the LHC. We begin with a careful Tevatron analysis, considering in general which sets of effective vertices give rise to a large forward-backward asymmetry while suppressing the contribution to the total t¯t cross-section. We show on general grounds that scalar models struggle to produce sufficient asymmetries consistent with CDF observations, while vector models can produce a large asymmetry with a less significant tension in the total cross-section and t¯t invariant mass distribution at the Tevatron. We examine the essential observables of these models for top physics at LHC7 with 1 fb−1 of data, including the total cross-section, invariant mass distribution and number of additional jets in t¯t events. In the case of t-channel mediators, the LHC total cross-section places a strong constraint on light mediators, while the Tevatron invariant mass distributions place strong constraints on heavy mediators that are able to produce the asymmetry. Heavy axigluons are becoming increasingly squeezed by LHC7 t¯t and dijet resonance searches. We conclude that LHC7 top analyses are rapidly closing the window for viable models of the CDF top AFB.

I Introduction

The Large Hadron Collider (LHC) is providing an unprecedented probe of top quark properties.
While the Tevatron has to date collected on the order of a thousand tops, the LHC, with 1 fb−1 of data has already nearly an order of magnitude more tops. The improvement is due both to a larger production cross-section, and to improved rapidity coverage for leptons in semi-leptonic and fully leptonic top analyses. In terms of the percentage error on the total cross-section, the 7 TeV LHC (LHC7) results are already competitive with the Tevatron cdftotalxsection with only 35 pb−1CrossSection , while the invariant mass distribution with just 200 pb−1 extends to a higher mt¯t of 2.5 TeV InvariantMass as compared to the Tevatron reach of 1.8 TeV Aaltonen:2009iz . At 1 fb−1, the top quark properties will be far better measured than at the Tevatron.

At the same time, the Tevatron as a p¯p machine is better able at the outset to measure a forward-backward asymmetry.111Though see Hewett:2011wz ; Bai:2011uk for efforts to make a measurement of the forward-backward asymmetry at the LHC. The asymmetry in a particular invariant mass bin, mt¯t,i, is defined by

with Δy the rapidity difference between a top and an anti-top. The recent CDF anlaysis shows AFB=0.475±0.114 for mt¯t>450 GeV Aaltonen:2011kc at the parton level (or AFB=0.266±0.062 at the signal level)222Throughout this paper we use “signal level” to refer to background subtracted, raw measured quantities in the detector, and “parton level” to refer to unfolded results which attempt to subtract detector effects from the results., while the Next-to-Leading Order (NLO) Standard Model (SM) predicts much lower values 0.088±0.013 (or 0.043±0.009 at the signal level) Kuhn:1998jr ; Kuhn:1998kw ; Bowen:2005ap ; Almeida:2008ug ; Ahrens:2011uf , corresponding to a 3.4σ deviation (3.6σ at signal level). A measurement of the asymmetry with fully leptonic tops has also been made which is roughly consistent with the measurement in the semileptonic channel CDFLeptons . The D0 collaboration also observes a larger than predicted asymmetry Abazov:2007qb .

There are a large number of possibilities for the spin, color, flavor and electroweak representation of a new field that fits into the two categories mentioned above.
In the literature these have been mostly built and studied one by one. Here, by contrast, we are motivated to extract general features to determine which effective vertices are able to generate the large AFB while contributing a small amount to the total cross-section. We find that the form of the matrix element itself allows one to make general conclusions about which classes of models are successful in generating a significant asymmetry.

We find on general grounds that perturbative444Scalar models with larger couplings can achieve larger asymmetries, though at the expense of a larger contribution to the total t¯t cross-section. scalar models typically can produce no more than a 10−20% “parton level” asymmetry for mt¯t>450 GeV, which is only somewhat larger than the asymmetry produced in the SM (at ∼9%) and well below CDF’s parton level central value of ∼48%.555The data-level asymmetry yields a result about a factor of two lower than the parton level result, which has been confirmed by the theoretical study of Gresham:2011pa . A comparison of a parton level theoretical result to the signal level asymmetry is not valid, and will underproduce by more than 2σ the observed asymmetry. The reason is simply the combination of the Mandelstam variables that enters into t- and u-channel processes for scalars; the statement is independent of the color (singlet, triplet, sextet or octet) or flavor representation of the state. By contrast, t-channel vectors have a matrix element that is conducive to producing a large asymmetry with a relatively small contribution to the total cross-section.

We systematically enumerate the possibilities for the quantum numbers of t- and s- channel mediators that can produce an asymmetry and show that classes of models are strongly disfavored based on a small contribution to the total asymmetry or large contribution to the total t¯t cross-section at the Tevatron. This paper is intended to be a companion to our earlier paper on AFBGresham:2011pa , which carried out a systematic comparison of NP models to the data. This was the only theory paper to carry out the full top reconstruction in order to compare results at the signal level. We found that there were large acceptance effects which changed the extracted parton level comparison between the SM and the NP models.666See also Jung:2011zv for a discussion of the acceptance effect at the parton level.

With LHC data quickly arriving, however, the source of strong constraints is rapidly changing, and we are particularly compelled by the fact that the LHC collaborations are now analyzing unprecedented amounts of top data that will clearly rule out a large swath of models. We examine observables from the LHC, such as total cross-section, t¯t invariant mass distribution, and the number of additional jets in t¯t events. In order to carry out our analysis, we have done a systematic scan in mass and coupling space for a broad class of models, described in appendix B. For a subset of the models that give the best fit to the data we generate 5 million events, applying cuts and mt¯t reconstruction mirroring the ATLAS analysis InvariantMass in order to compare to LHC t¯t distributions. Many models will be strongly constrained by these analyses with just 1 fb−1.777These statements must take into consideration, however, uncertainties in next-to-leading-order (NLO) corrections to the NP contributing to the total cross-section and invariant mass distribution. In our earlier paper on searching for flavor-violating resonances at the LHC, we proposed top-jet resonances as a means to search for t-channel mediators Gresham:2011dg . Such a search is complementary to the analysis here. Many t-channels models will be constrained by existing analyses, but the models that survive can have an imprint in top-jet resonances.

The outline of this paper is as follows. In the next section we discuss the classes of models that could generate the forward-backward asymmetry at the parton level, examining the asymmetries that are generated by the possible effective vertices, and drawing conclusions about which classes of models are viable. The reader who is interested only in the numerical results can skip this section, and move on to Sec. III, referring to Sec. (II) solely for a discussion of our conventions. In Sec. (III), we carry out a systematic scan of models at the Tevatron, choosing a set of models as benchmarks for simulation of the large data sets necessary for invariant mass distributions. In Sec. (IV), we then examine the expected top properties at the LHC for the classes of models we consider. In the appendices, parton level asymmetries, as well as a detailed discussion of our analysis pipeline, can be found.

Ii Effective Vertices and Top Afb

Broadly speaking, either s-channel or t- (or u)-channel resonances can generate the top forward-backward asymmetries at tree level. We show the diagrams that contribute both to the Tevatron AFB and t¯t production at LHC in Fig. 1. The structure of the differential cross-section for models that produce the asymmetry through t-channel exchange of a top-flavor-carrying mediator takes the same basic form according to whether the mediator is spin-0 or spin-1. Let the effective Lagrangian involving top and up quarks take the form

where ~t=t for singlets and octets and ~t=tc for anti-triplets and sextets, and tar are the color generators of a representation r—3×3 Hermitian matrices that contain Clebsch-Gordon coefficients connecting two (anti-)quarks, normalized so that Tr(tartbr)=12δab. For singlets, we take tar=1. Note that we are restricting ourselves to couplings to top and up quarks, though our results should not qualitatively change given couplings to down-type quarks. We also only consider single mediator production; double mediator production is only important for light colored states, which are not present for the models we consider.

A large number of models of NP can generate these effective vertices, involving, in addition to the color group, potentially SU(2) and flavor representations. There are a limited number of flavor symmetric models that can generate the top AFB in the t channel while satisfying existing constraints. We show in Table 1 the possibilities. There are also interactions that connect QL to QL, but these models with flavor symmetries are typically highly constrained by light quark observables since they mix with SM CKM physics. We do not consider them further. Interactions connecting, e.g., QL to uR through a spin-1 color triplet or sextet “diquark” are also possible, but as we will soon see (see Fig. 6), the dominant t-channel interaction for top AFB does not give rise to a significant positive asymmetry. We refer the reader to Arnold:2009ay ; Giudice:2011ak for a complete tabulation in the scalar mediator case of the possible flavor symmetries and to Grinstein:2011yv ; GrinsteinToAppear for discussion of AFB in the context of Minimal Flavor Violation. In any case, the general observations that we make on the basis of the effective vertices in Eq. (2) will be relatively independent of the flavor representation, and we make the appropriate qualifications where necessary. For example, in flavor symmetric models, states in both the t channel and the s channel can contribute to the total asymmetry. Scalars in the s channel don’t contribute to the forward-backward asymmetry, but can have an impact through their interference with t-channel scalars that do generate the asymmetry.

Interaction

SU(3)c

SU(2)

U(1)Y

Flavor (uR,dR,QL)

¯uRQL

1, 8

2

±1/2

(3,1,¯3)

uRuR

3,¯6

1

-4/3

(3,1,1)

dRuR

3,¯6

1

-1/3

(3,1,1)

¯uRγμuR

1,8

1

0

(1,1,1)

¯uRγμuR

1,8

1

0

(8,1,1)

¯dRγμuR

1,8

1

-1

(¯3,3,1)

Table 1: Flavor symmetric interactions (in schematic notation) involving at least one uR quark that can mediate a significant positive top forward-backward asymmetry in the t-channel. (See also GrinsteinToAppear .)

Given the large number of possible combinations of s- and t-channel resonances from the flavor symmetric models, one despairs of ever being able to derive the characteristics of the state that can generate the asymmetry. However, we will find that in the t (or u) channel, the amplitudes have very distinctive shapes dependent on whether the state is a vector or scalar mediator particle. We examine these characteristic features, and use it to draw conclusions about the nature of the mediator from the invariant mass dependence of AFB. These conclusions are robust independent of the particular flavor symmetric model that one employs, and allows one to make general statements on the types of characteristics that are necessary for generating a large top AFB.

The cross-sections arising from the NP interactions (2) and SM interactions are given by

Here Cr(0) and Cr(2) are color factors depending on the color rep of the mediator.888Specifically, Cr(0)=−ξTr(tarTAtar~TA) and Cr(2)=Tr(tartbr)Tr(tartbr) where ξ=−1(1) and ~TA=TA(TAT) for octets and singlets (anti-triplets and sextets).
We have also defined

cθ=βcosθβ=√1−4m2t/^s,

(7)

^ti≡^t−m2i^ui≡^u−m2i.

(8)

The Mandelstam variables are related to the scattering angle via

^t=−^s(1−cθ)/2+m2tand^u=−^s(1+cθ)/2+m2t.

(9)

Note that we have not taken into account interference between NP contributions which can arise in flavor symmetric models. For example, s-channel flavor conserving and t-channel flavor changing diagrams may interfere. These new contributions do not give rise to any new types of terms (modulo mass terms in propagators) in the interference amplitude for the vector states, but do give rise to new contributions for the scalar states. We discuss these terms later, but suffice for now to comment that the new terms will not change our qualitative conclusions.

For a color singlet rather than a color octet, the interference term vanishes and the squared term is scaled by a factor C1(2)/C8(2)=9/2.

We now assemble these results using the parton distribution functions to gain a strong quantitative understanding of which types of interactions can give rise to the observed forward-backward asymmetry.
The cross-section for the process p¯p→t¯t is given by:

σ(s)=Σi,j∫d^s∫1^s/sdx1sx∫dcosθfi(x)fj(^ssx)^σi,j(cosθ,^s).

(14)

We define

Fij(^s,s)=∫1^s/sdx1xfi(x)fj(^ssx).

(15)

Then the differential cross-section as a function of parton energy ^s can be expressed as

dσ(s)d^sdcosθ=1sΣi,jFij(^s,s)^σi,j(cosθ,^s).

(16)

Of course, all the cosθ dependence is in the parton-level differential cross-section. If only one kind of initial state parton contributes to the cross-section, then the PDF completely factors out of the differential forward-backward asymmetry, defined as a function of ^s by

AFB(^s)=Σi,jFij(^s,s)^σ−i,j(^s)Σi,jFij(^s,s)^σ+i,j(^s),

(17)

where

^σ±i,j(^s)≡∫10dz(^σi,j(z,^s)±^σi,j(−z,^s)).

(18)

Figure 2: SM contribution to the denominator in the differential forward-backward asymmetry as defined in (18). CTEQ5M parton distribution functions were used.

Suppose we are interested in a NP model with a nonzero contribution to the cross-section term generated through u¯u→t¯t. We may then write the forward-backward asymmetry as a function of √^s as

AFB(^s)=^σNP−u¯u^σNP+u¯u+SM contribution,

(19)

where

SM contribution=^σSM+u¯u+Fd¯dFu¯u^σSM+d¯d+FggFu¯u^σSM+gg,

(20)

and is shown in Fig. (2).
We note here that the falling SM contribution alone is not enough to give as steep a rise in the asymmetry as a function of ^s as is observed at CDF. The rise can steepen through a combination of the following factors: (1) ^sβ^σNP−u¯u rises as a function of ^s and/or (2) ^sβ^σNP+u¯u is comparable to the SM contribution and decreases as a function of ^s. However, if the majority of the steepness were to come from mechanism (2), the total cross-section especially at low invariant mass would have to be comparable to the SM cross-section; this is hard to do without running into constraints on the total differential cross-section. Thus a significant contribution must come from ^σNP−u¯u.

There are seven kinds of terms that show up in a general cross-section involving t-channel mediators, including its interference with the SM:

with ^t↔^u for or u-channel diquarks.
We examine these contributions term by term to determine which types can successfully generate a large contribution. In particular, there must be a large contribution to the asymmetry with a very modest contribution to the total cross-section. That is to say simply that the odd contribution must be large in comparison to the even contribution.

We examine this in detail in Fig. (3) for different types of effective vertices. The salient points to take away from the figures are: (1) Scalars have odd contributions comparable to vectors only in the higher mediator mass range. (2) As a function of energy, the magnitude of the odd term for a given contribution is never greater than the magnitude of the even term, though some terms obtain much closer to equal magnitudes than others. Thus in order to best succeed in generating a sizable positive asymmetry while not destroying the invariant mass distribution, an ideal model will involve destructive interference between the even parts of the SM-NP interference and NP squared terms of the amplitude, and minimal or constructive interference between the odd part of the SM-NP interference and NP squared terms.999That some amount of destructive interference is favored by the data was noted in Grinstein:2011yv . By inspection, none of the scalars (t or u-channel) can satisfy this condition. Scalar diquarks have some success in generating a substantial asymmetry in an intermediate mass range where the squared term contributes the dominant positive odd contribution. For the triplet, the interference term gives a negative odd and even contribution (so it helps to lower the cross-section but also lowers the numerator) while for the sextet the interference term enters with a minus sign and so gives a positive odd and even contribution (so it increases the numerator but also the cross-section).

Figure 3: Terms contributing to cross-sections with t or u channel mediators. Solid lines indicate the odd contribution and dotted the even contribution, integrated over cosθ. The top plots include terms from the interference term, and the bottom plots from the NP squared term. For diquarks, ^u↔^t, which flips the sign of the odd contribution and leaves the even contribution the same. The letters in square brackets indicate whether the term appears for scalar [S], vector [V], or both [S,V] mediators.

For vectors there are more terms in play, so the story is a bit more complicated. To show the effects on the total asymmetry, we plot the total asymmetry (and, when relevant, cross-sections) for all t- and u-channel mediator color representations and spin combinations in Figs. (4)-(6). We show three benchmark mediator masses. Fig. (4) shows the scalar models that succeed in generating a positive asymmetry, though in general for perturbative couplings it is not a large positive asymmetry; Fig. (5) shows the same for the vector mediator case, and it is seen that the contribution to the total asymmetry can be large for all mass ranges. Lastly, we show in Fig. (6) the mediators that fail to produce a positive asymmetry larger than 5%. These include the scalar color octet and vector triplet and sextet.

Figure 4: Spin-0 mediators. Left-hand plots show the differential asymmetry for various couplings given a 150 GeV, 400 GeV or 800 GeV mediator. A line is drawn at √^s=450GeV to highlight the value of the asymmetry at the lower end of the the CDF analysis higher invariant mass bin. Due to the rapidly falling PDFs, the high invariant mass bin asymmetry will be given roughly by the value of the differential asymmetry at 450 GeV. The right-hand plots show contributions to the parton level u¯u→t¯t cross-section as a function of √^s (dotted lines), and to the odd parton level cross-section (forward - backward), normalized by 32π^s/β to make a dimensionless quantity. The effective Standard Model contribution as defined in (20) is shown as a black dotted line. Contributions to the total differential cross-section, dσi(s)/d^s, can be obtained from the dotted contributions by multiplying by the factor βFu¯u32πs^s. (See Eqs. (16) and (19))

Figure 5: Spin-1 mediators. Left-hand plots show the differential asymmetry for various couplings given a 150 GeV, 400 GeV or 800 GeV mediator. A line is drawn at √^s=450GeV to highlight the value of the asymmetry at the lower end of the the CDF analysis higher invariant mass bin. Due to the rapidly falling PDFs, the high invariant mass bin asymmetry will be given roughly by the value of the differential asymmetry at 450 GeV. Right-hand plots show contributions to the parton level u¯u→t¯t cross-section as a function of √^s, as in Fig. 4. The Standard Model contribution as defined in (20) is shown as a black dotted line.

Figure 6: The asymmetry for representations that cannot produce a positive asymmetry of more than a few percent.

One might wonder whether the asymmetry induced by scalars could be enhanced by adding another scalar with s-channel couplings to u¯u and t¯t. This is predicted, for example, by the flavor triplet models. Interference between a t-channel scalar with mass m1 and an s-channel scalar with mass m2 would give rise to terms of the form ^s^tt(^s−m22)^t1 and ^sm2t(^s−m22)^t1. These contributions, assuming m1=m2, are shown in Fig. (7). For mediators lighter than the top quark, the odd contribution has the same sign as even for both terms, and it is hard to see how these contributions can enhance the asymmetry while not increasing the total cross-section to unacceptable levels.
For mediators heavier than the top quark, odd and even contributions for the ^s^tt/(^sM^tM) have the opposite sign—the odd contribution is positive for energies below the mediator mass and negative above. This interference could have interesting implications for models involving both t-channel and s-channel scalars of intermediate mass. Diquarks with s-channel interactions would not contribute to the t¯t cross-section or AFB.

Figure 7: Terms contributing to s-channel scalar / t-channel scalar interference cross-section. Solid lines are the odd contributions and dashed are the even contributions, integrated over cosθ. Here we assume a narrow width.

Lastly, we briefly discuss s-channel mediators, which can give rise to a large asymmetry for an appropriate choice of couplings and masses. If the asymmetry is generated from s-channel NP interactions, then the cosθ dependence of the NP cross-section is a simple quadratic polynomial. The axigluon originally proposed in Ref. Ferrario:2009bz ; Frampton:2009rk supposed a heavy axigluon to evade dijet and t¯t resonance searches that strongly constrain the state with masses below ∼2 TeV. However, recently different regions of the axigluon parameter space have been explored. For example, a 750 GeV state was considered in AguilarSaavedra:2011ci , with the dijet constraints evaded by making the coupling to the top quark much larger than to the up quarks. A 400 GeV state was considered in Tavares:2011zg , and the t¯t resonance search constraints evaded by making the state sufficiently broad. Lastly, if a vector with diagonal axial couplings to top and up has a mass slightly lighter than the top mass, then it will not show up as a resonance in the t¯t spectrum. We refer the reader to these references for details, though we include the axigluons in our scans of parameter space in the next section for completeness.

Iii Comprehensive Search for Models at the Tevatron

To augment the conclusions of the previous section, we carry out a comprehensive representative scan of models using MadGraphAlwall:2011uj ; the details of our procedure are discussed in Appendix B.
We scan over s,t,u-channel models, characterized by a single new mediator of given spin and color representation (2); we scan over all such models that can produce a positive asymmetry of more than a few percent while remaining (somewhat) perturbative (coupling ≲6) and contributing less than order 50% to the total cross-section in the mass range 200 GeV - 2 TeV.101010We neglect models with mass below the top (e.g.Jung:2011zv ); in general, these models will tend to rather severely overproduce the total cross-section and number of additional jets at the LHC and/or lead to large contributions to single top production, depending on the details of the mediator decay channels. The models scanned are summarized in Table 3. We choose representative models that generate the largest asymmetry. For t-channel models we focus on mediators connecting up to top, both because they generate a large asymmetry, and also because a light neutral state runs into few constraints. The color singlet and triplet are our representative scalar models, though neither is successful in generating a large asymmetry, as we detailed earlier. Also note that the singlet scalar is part of an electroweak doublet, though we choose to couple this scalar to tL−uR so that only one state is operative for the forward-backward asymmetry. The charged component of the SU(2) mediator multiplet will contribute to b¯b plus jet events at the LHC, but this will be easily overwhelmed by the background. For the t-channel flavor-violating models, we consider both a color singlet vector (C1V) and octet vector (C8V) that couples only to right-handed states. We also consider a flavor octet, color singlet vector (F8C1V) that couples to ¯URγμUR, where now the up quarks are in an octet of SU(3)UR. Lastly, the s-channel axiglue type models are considered, both in flavor universal Tavares:2011zg and non-universal Frampton:2009rk ; AguilarSaavedra:2011ci varieties.

Table 3: Summary of models scanned. All t- or u- channel states are taken to be non-self-conjugate.

The results of this scan for the Tevatron are shown in Figs. (8) - (10). The coupling conventions in the figures are as follows. The t-channel scalars, as well as C1V and C8V, models are labeled by their coupling to RH quarks, with gL=0. The flavor symmetric F8C1V model has an additional parameter η that controls the flavor breaking coupling to the top quarks such that couplings to top-quarks have couplings ∼gR+2ηm2t/v2, with v=246 GeV. The coupling conventions for s-channel models are more complicated. The couplings in schanC8VΓ and schanC8VA are purely axial (gR=−gL), with the former only being flavor universal. The schanC8VΓ model has an independent width parameter Tavares:2011zg , which was scanned over to find models with maximally large asymmetries per unit production cross-section. schanC8VR has non-universal couplings to right-handed quarks AguilarSaavedra:2011ci .

Figure 8: Scatter plots depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×acceptance} at Tevatron CM energy for t-channel flavor-changing scalar models listed in Table 3. The models are labeled by the mass of the mediator, the coupling to right-handed quarks, and the total Tevatron production cross-section times acceptance. The cross-sections are compared against the SM cross-section times acceptance which yields 0.252 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color. Figure 9: Scatter plots depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×Acceptance} at Tevatron CM energy for t-channel flavor-changing vector models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total Tevatron production cross-section times acceptance. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section times acceptance which yields 0.252 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color. Figure 10: Scatter plots depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×Acceptance} at Tevatron CM energy for axigluon models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total Tevatron production cross-section times acceptance. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section times acceptance which yields 0.252 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color.

We apply cuts on the simulated sample and fully reconstruct tops as described in Appendix B to mimmic the analysis in Aaltonen:2011kc .
More specifically, for Tevatron events we apply the following sets of cuts:

Exactly one electron or muon with pT>20 GeV and |η|<1.0.

At least four jets with pT>20 GeV and |η|<2.0, with at least one of the jets having a b-tag.

EmissT>20 GeV.

We reconstruct tops as described in Gresham:2011pa , doing a likelihood analysis on the lepton and jet kinematics to the t¯t hypothesis, using the algorithm described in our previous paper Gresham:2011dg .
The cone jet algorithm was used for Tevatron events. Jet energy scale corrections were carried out via a procedure described in Appendix B.

We choose to show results after detector simulation (at the signal level) because, as discussed in Gresham:2011pa , unfolding of data to the parton level is model dependent. In Figs. (8-10) the axes give the signal level AFB with mt¯t<450 GeV and mt¯t>450 GeV. The ellipses encircle the best fit points to the CDF signal level semileptonic t¯tAFB with concentric ellipse giving χ2/d.o.f.=1,2,3, with the constraints from the total cross-section times acceptance being taken into account via

as the central values. Note that the last value is the central LO SM cross-section times acceptance, given the cuts for Tevatron and LHC7 outlined in this section and the next. The central values for AFB are the background-subtracted signal level values from Aaltonen:2011kc and the SM values for the cross-section times acceptance are taken from our simulations of 5 million events.
The first two contributions to the AFB errors are from experiment, the third for the typical statistical error from our finite-sized simulated data samples, and the last is to account for possible NLO corrections: we take this contribution to be of the same size as the NLO SM asymmetry. For the cross-section error, we take 15% errors for the Tevatron and 10% for LHC. 10% is roughly the current experimental error for the Tevatron measurements, and we add a ∼5% uncertainty due to the top mass and theory uncertainties in the NLO corrections. For LHC, the statistics on the cross-section measurement should lead to smaller error bars and we take this into account with a smaller LHC error of 10%. A value χ2∼3 indicates a good fit to data. For the Standard Model with AFB given by the NLO prediction and cross-section by our LO simulations, χ2/3=2.8. Since we take the central value for the cross-section to be the SM LO value, this value is somewhat artificially low. These error estimates should be taken as rules of thumb to guide the eye in our figures for comparing SM against NP, rather than as hard and fast quantitative error budgets.

We discuss the scalar models first. As can be seen from Fig. (8), the triplet scalars generally produce larger asymmetries than singlet scalars, which generally cannot produce a larger asymmetry than the SM. This can be qualified if the singlet scalars are lighter than the top mass, in which case signal level asymmetries as large as 10% for mt¯t>450 GeV can be achieved (though this is well below what is observed). This in agreement with the parton level results of Nelson:2011us , taking into account the factor ∼2 washout translating from parton level to signal level. The triplet scalars seem to reproduce the total asymmetry and cross-section very well. However, it was shown in Gresham:2011pa that these models seriously overproduce the invariant mass distribution at large invariant mass. We refer the reader to Gresham:2011pa for details.

Next we discuss the t-channel vector mediators in Fig. (9). As expected from the results in Gresham:2011pa , the color singlet vector is most successful in reproducing the asymmetry at high invariant mass and satisfying the cross-section constraints. Due to details in the form of the matrix element, the color octet is less successful. The flavor universal octet can produce large asymmetries, but these also tend to come with fairly large contributions to the total cross-section, due to the presence of both s and t-channel mediators.

Lastly, we discuss the s-channel states in Fig. (10). The wide, low mass axiglue models, schanC8VΓ, in general are most successful at producing a large asymmetry with small contribution to the total cross-section. The light axigluon models with couplings to right-handed quarks and masses in the 700-900 GeV range (schanC8VR) AguilarSaavedra:2011ci do not produce a large asymmetry on the other hand; in most cases it is not larger than the SM asymmetry. Heavy axigluon models can succeed with a large enough coupling to light quarks, but these risk being ruled out shortly by LHC dijet and t¯t resonance searches.

With these results in hand, we now turn to examining the implications of models that are capable of satisfying the Tevatron constraints on top analyses at LHC7. For each class of models, and a selection of mediator masses between 200 GeV and 2 TeV, we take models with the lowest χ2 as defined by the statistic in Eq. (22). 5 million events are generated for each of these benchmark models to gain enough statistics at the high invariant mass, via the procedure in Appedix B. Our benchmark models are not an exhaustive set of model choices, but they are indicative of the types of models that can generate top AFB. The choice of models is shown in Table 4. It gives the mass and coupling of the model, the LO cross-section at Tevatron and LHC along with the acceptance A., the signal and parton level AFB in the low and high invariant mass bins, along with the total asymmetry, and the χ2 at Tevatron and LHC, using the statistic discussed in the text. These results are to be compared against the SM, shown in Table 5.

Note that the models with the lowest χ2 tend to universally underproduce the total asymmetry. The reason is that the models with the largest AFB also tend to overproduce the total cross-section rather seriously, so that the χ2 prefers to take a hit on the asymmetry (which has 1σ errors of ∼8% at the signal level) in lieu of a large t¯t production cross-section. The models that are the least successful at producing a large asymmetry with minimal impact on the total cross-section are: C8V, C1S, schanC8VR. These models are generally able to produce little more than the SM asymmetry for AFB with mt¯t>450 GeV, and should not be considered as viable models for AFB.

signal level

parton level

parameters

σTev (pb), A.

σLHC (pb), A.

A<450FB, A>450FB, AtotalFB

A<450FB, A>450FB, AtotalFB

χ2Tev, χ2LHC

m, gR

C1V

200., 0.7

6.3, 0.037

146, 0.068

-0.03, 0.15, 0.06

0.01, 0.39, 0.2

0.8, 2.3

400., 1.3

7.1, 0.038

154, 0.073

0.01, 0.25, 0.15

0.08, 0.55, 0.35

0.2, 4.7

600., 1.5

5.3, 0.039

126, 0.072

-0.04, 0.15, 0.06

-0.03, 0.25, 0.1

1.2, 1.2

800., 2.1

5.8, 0.039

129, 0.073

-0.03, 0.18, 0.09

-0.01, 0.36, 0.18

0.5, 1.1

m, gR

C8V

400., 0.75

6.8, 0.041

130, 0.072

0.01, 0.08, 0.04

0.03, 0.1, 0.06

2.1, 2.7

800., 1.4

6.8, 0.04

120, 0.072

-0.01, 0.08, 0.03

0.03, 0.1, 0.06

1.9, 2.

m, g, η

F8C1V

200., 0.5, 1.

6.5, 0.037

148, 0.067

0.05, 0.14, 0.09

0.03, 0.4, 0.21

1.4, 2.8

400., 0.5, 0.

9.4, 0.04

125, 0.069

0.08, 0., 0.05

0.23, -0.02, 0.17

8.5, 5.1

600., 0.5, 3.

6., 0.041

128, 0.071

-0.03, 0.15, 0.07

-0.05, 0.31, 0.14

0.7, 1.1

800., 0.5, 1.

6., 0.041

115, 0.072

-0.03, 0.01, -0.01

0., 0.03, 0.01

3.5, 3.5

m, gR

C1S

200., 1.5

5.7, 0.042

119, 0.072

0.01, 0.04, 0.03

0., 0.06, 0.02

2.9, 3.

m, gR

C3S

400., 2.95

8.6, 0.033

165, 0.074

0., 0.17, 0.11

0.2, 0.22, 0.21

0.8, 8.4

600., 3.4

6.7, 0.043

133, 0.075

0., 0.14, 0.08

0.05, 0.23, 0.14

1.2, 2.6

800., 4.15

6.6, 0.042

128, 0.075

-0.01, 0.15, 0.08

0.03, 0.27, 0.15

0.9, 1.8

m, gR, Γ/m(%)

schanC8VΓ

420., 0.45, 18

6.7, 0.04

116, 0.072

-0.03, 0.15, 0.05

-0.03, 0.3, 0.1

0.8, 0.8

440., 0.45, 13

6.9, 0.039

118, 0.07

-0.03, 0.12, 0.04

-0.11, 0.34, 0.06

1.1, 1.1

m, gqR, gtR

schanC8VA

2000., -1., 5.

6.4, 0.04

117, 0.072

0.01, 0.16, 0.08

0.06, 0.17, 0.1

0.7, 0.8

2400., -3.6, 3.6

6.5, 0.039

119, 0.072

0., 0.14, 0.07

0.07, 0.21, 0.13

1., 1.

m, gqR, gtR

schanC8VR

700., -0.05, 4.5

6.7, 0.04

116, 0.07

0., 0.06, 0.02

0.02, 0.07, 0.04

2.4, 2.4

850., -0.08, 6.

6.7, 0.039

117, 0.072

0.04, 0.08, 0.06

0.02, 0.08,0.04

2.2, 2.2

Table 4: A representative set of models chosen for LHC analysis. Acceptance is labeled “A.”.

LO SM cross-section, NLO AFB

signal level

parton level

σTev (pb), A.

σLHC (pb), A.

A<450FB, A>450FB, AtotalFB

A<450FB, A>450FB, AtotalFB

χ2Tev, χ2LHC

6.3, 0.04

115, 0.071

0.015, 0.043, 0.024

0.040, 0.088, 0.058

2.8, 2.8

Table 5: The SM LO cross-section at Tevatron and LHC along with the acceptance, A., the signal and parton level AFB in the low and high invariant mass bins, along with the total asymmetry, and the χ2 at Tevatron and LHC, using the statistic discussed in the text.

Before moving on to the LHC analysis, we check the Tevatron invariant mass distributions for the classes of models that we examine more carefully. As we learned in Gresham:2011pa , acceptance effects can be important in bringing NP models into agreement with the Tevatron invariant mass distributions. We show the Tevatron invariant mass distributions in Figs. (11)-(12), for comparison to the LHC results we discuss next.

Figure 11: Tevatron invariant mass distributions, on both linear and log scales, for our benchmark models choices. The SM is shown in the yellow band, with statistical errors for 5.3 fb−1 of data.

Figure 12: Tevatron invariant mass distributions, on both linear and log scales, for our benchmark models choices. The SM is shown in the yellow band, with statistical errors for 5.3 fb−1 of data.

Iv Implications for Top Physics at the LHC

For the LHC benchmark points analysis, we generate 5 million events for each model, as we did for the Tevatron analysis. We also modified the PGS code to implement the anti-kT algorithm Cacciari:2008gp to mimmic ATLAS as detailed in Appendix B.
In the following, closest attention should be paid to the C1V, F8C1V, C3S, schanC8VΓ and schanC8VA models, as these, among the models in the literature we have considered, are able to generate the top AFB to a reasonable degree.

The variables that we focus on at the LHC are:

Total cross-section. The chief uncertainties here come from NLO corrections from both the SM and NP, and the uncertainty in the top mass;

Invariant mass distribution. Here again NLO corrections will play an important role;

Number of additional jets. In t-channel models, single production of the mediator in conjunction with the top is an important process at the LHC. A gluon and light quark in the initial state will exchange a top in the t-channel and produce a top along with a mediator as in Fig. (1). The mediator will prefer to decay to a top and another jet, leading to a potential enrichment of events with an extra jet. The direct search for the top-jet resonance as a signature for these models was studied in Gresham:2011dg , but its presence may be known through counting the number of additional jets in t¯t events.

Rapidity distribution of the lepton. Especially for models with a t-channel resonance, the leptons may be produced in a more forward direction at the high invariant mass. On the other hand, single mediator production leading to t¯t+jets events can lead to more central leptons.

We follow the cuts discussed in the 200 pb−1 ATLAS semileptonic top analysis InvariantMass . We require:

exactly one electron with pT>25 GeV and |η|<2.5, or exactly one muon with pT>20 GeV and |η|<2.5;

at least four jets with pT>25 GeV and |η|<2.5, one of which must be b-tagged;

if the lepton is an electron, we require EmissT>35 GeV and the transverse mass of the lepton and EmissT be greater than 25 GeV; if the lepton is a muon, we require EmissT>20 GeV and the transverse mass of the lepton with EmissT, plus the EmissT, be greater than 60 GeV;

jets within ΔR<0.2 are removed so as to avoid double-counting of electrons as jets.

In addition, ATLAS demands isolation cuts; since we do clustering in PGS before placing the cuts, we do not apply them.
mt¯t is re-constructed in the same way as ATLAS, carried out without a full top reconstruction. The neutrino momentum is found assuming the W mass and massless neutrino conditions. For some events there is no positive energy solution, in which case the event is discarded. According to the ATLAS analysis, we take the longitudinal neutrino momentum to be the real part of the mass constraint solution in the case of imaginary solutions and we take the solution with smallest absolute value if there are two solutions.

The first and simplest measure is the top forward-backward asymmetry versus the total production cross-section at the LHC. There is a trade-off between models with a large enough coupling to produce the observed forward-backward asymmetry, while simultaneously having a small enough coupling that single mediator production at the LHC does not lead to a large contribution to the t¯t cross-section. However, given that the higher mass models in particular have large couplings, one expects the next-to-leading-order (NLO) corrections to play a significant role in both the total cross-section and invariant mass distributions. Given the gross-overproduction of some models of the total cross-section, some may, however, be reasonably eliminated. This can be seen in Figs. (13-15), where we plot the Tevatron AFB in low and high invariant mass bins, with total production cross-section at LHC times acceptance indicated by color. We again compare LO MadGraph results against the LO SM cross-section times acceptance (28). We find a total LO matched SM t¯t+0or1 jets cross-section of 115 pb for mt=172 GeV. Note that there is a large K-factor of ∼1.6 expected at LHC7 which enters to match the total cross-section observed (of about 180 pb) against the LO contribution. The LO cross-section times acceptance is 8.178 pb.

Figure 13: Scatter plot depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×acceptance} for t-channel flavor-changing scalar models listed in Table 3. The models are labeled by the mass of the mediator, the coupling to right-handed quarks, and the total LHC production cross-section times acceptance. The cross-sections are compared against the SM cross-section times acceptance which yields 8.178 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color. Figure 14: Scatter plot depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×Acceptance} for t-channel flavor-changing vector models models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total LHC production cross-section times acceptance. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section times acceptance which yields 8.178 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. Model points of a given color should be compared to χ2 contours of the same color. Figure 15: Scatter plot depicting simulated signal level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t×Acceptance} for axigluon models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total LHC production cross-section times acceptance. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section times acceptance which yields 8.178 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. Model points of a given color should be compared to χ2 contours of the same color.

A couple of features in Figs. 13-15) in particular are worth highlighting. t-channel models at the LHC overproduce the total cross-section much more than at the Tevatron. This is because single production of the t-channel mediators gives rise to a significant contribution to the total cross-section. This effect is more important for lighter mediators, so that light mediators become much more disfavored at the LHC.

Note that this brings in a significant tension for t-channel models of AFB between the constraints from Tevatron and the LHC. The Tevatron t¯t invariant mass distribution tended to favor lighter mass mediators because they lead to less distortion of the invariant mass distribution at high invariant mass Gresham:2011pa , while LHC favors heavier mediators because they lead to less distortion in the total cross-section.

We next consider the effect on the invariant mass distribution for our benchmark models. The results are shown in Figs. (16), (17). The effect of the NP on the shape of the invariant mass distribution is very different at the LHC than at the Tevatron. At the Tevatron, the effects of the new mediator become most pronounced at the high invariant mass—for the t-channel models in particular. At the LHC, this effect is not present, because most of the impact of the new mediators on the cross-section is simply single mediator production. The s-channel models with a sufficiently broad width have little impact on the invariant mass distribution. Thus it appears that most of the constraint on the new models comes simply from the total cross-section measurement. We also note that acceptance effects explored in Gresham:2011pa are not as important at LHC as at Tevatron, both because NP t¯t events at LHC are more central, and because the rapidity coverage for leptons at ATLAS and CMS is better than at Tevatron.

Figure 16: C1S, C3S, C1V, F8C1V models differential cross-section times acceptance (on both linear and log scales) at LHC7 versus reconstructed mt¯t, as compared to SM LO expectation, with ±1σ yellow bands corresponding to statistical error given 1fb−1. Models shown are those with the lowest χ2 for a given mass as defined in Eq. (22), except for the 600 and 800 GeV C1V models, which were chosen to have the lowest χ2 and be within 10% of the SM cross-section times acceptance at Tevatron.

Figure 17: C8V and schanC8 models differential cross-section times acceptance (on both linear and log scales) at LHC7 versus reconstructed mt¯t, as compared to SM LO expectation, with ±1σ yellow bands corresponding to statistical error given 1fb−1. Models shown are those with the lowest χ2 as defined in Eq. (22).

Perhaps the leading discriminant is simply the number of additional jets in the event, shown in Figs.(18), (19). While the overall production cross-section may be somewhat uncertain due to NLO corrections, leading to an uncertainty in the overall normalization of the NP curves, there is a significant difference in the ratio of the number of events with one extra jet to the number of events with no extra jets. In fact, all of the t-channel models that generate a large asymmetry significantly overproduce the number of events with one additional jet. One might wonder whether this effect could be reduced by allowing a significant branching fraction to light quarks; however in this case these events will contribute significantly to the single top analyses, which already with only 200 pb−1 of data have an uncertainty of only 40 pb singletop . In the case of a significant branching fraction of the mediator to light quarks, single mediator production will easily contribute a significant fraction of this cross-section, with even more severe constraints arising in the high HT tail of the distribution, as pointed out in Craig:2011an . For reference in these figures we have also shown the rapidity distribution of the leptons; single mediator production results in a more central lepton rapidity distribution.

Figure 18: Number of additional jets and lepton differential rapidity distribution of C1V, F8C1V and schanC8 models at LHC7, as compared to SM LO expectation, with ±1σ yellow bands corresponding to statistical error given 1fb−1. Models shown are those with the lowest χ2 as defined in Eq. (22).

Figure 19: Number of additional jets and lepton differential rapidity distribution of schanC8, C8V, C1S and C3S models at LHC7, as compared to SM LO expectation, with ±1σ yellow bands corresponding to statistical error given 1fb−1. Models shown are those with the lowest χ2 as defined in Eq. (22).

V Conclusions

We have carried out a comprehensive analysis of NP models for top AFB utilizing both Tevatron and the prospective LHC7 constraints with 1 fb−1. We considered effective vertices for all possible spin, color and flavor representations connecting top quarks with up quarks. We were able to show on general grounds why scalar mediated models have difficulty reproducing the observed asymmetry. We revisited the Tevatron signal level invariant mass distributions, as investigated in our earlier paper Gresham:2011pa . We found that the prospective LHC constraints on the total cross-section offer complimentary constraints to the Tevatron invariant mass distribution. In the case of t-channel mediators, the LHC total cross-section places a strong constraint on light mediators, while the Tevatron invariant mass distributions place strong constraints on heavy mediators that are able to produce the asymmetry. The vanilla t-channel models thus seem disfavored at present. Heavy, narrow axigluons (with masses ∼2 TeV) are currently becoming more tightly constrained with the recent LHC7 top results. A 400 GeV axigluon with large width and universal couplings to quarks appears at present to evade all existing constraints.

The LHC is rapidly closing the window on viable models for the top forward-backward asymmetry. More non-generic features, such as large widths as in the light axigluon discussed here, will be necessary to make viable models consistent with both the Tevatron top AFB and LHC top observables.

Acknowledgments: We thank Sunghoon Jung, Daniel Whiteson, and Dirk Zerwas for discussions. KMZ thanks the Aspen Center for Physics for hospitality while part of this work was being completed. The work of KMZ was supported in part by NSF CAREER award PHY 1049896. MG is supported by the Michigan Society of Fellows.

Note added 1: After the first version of this manuscript was completed,
a new result on top AFB from the D0 collaboration appeared Abazov:2011rq , in which
AFB in the high t¯t invariant mass bin is significantly lower than
that of the CDF result. As a result, the concentric χ2
contour ellipses in Figs. (8-10), (13-15), and (20-22) will move down and to the right when the CDF and D0 results are combined, so that
many model points in danger with CDF alone will have a significantly lower χ2. As a result, the best model point may change. We leave the analysis to a future
publication.

Note added 2: Because of the rapidly changing experimental results, we
will periodically update our results on a web page. This
website will also provide some figures not included in this paper. See
http://susy.physics.lsa.umich.edu/TopPhysics.

Appendix A Parton Level Asymmetries

As a complement to the Tevatron signal level asymmetries shown in Figs. (8)-(10), we show the parton level asymmetries, so that theorists can easily map signal level onto parton level for a broad range of models. These are shown in Figs. (20)-(22) for the same model points as in Figs. (8)-(10). Note in comparing the signal and parton level plots that a number of points are deleted in the parton level plot in cases where they cluster strongly around the SM point and become indistinguishable. For these parton level plots the χ2 statistic used to draw contours is defined in Eq. (22), but with

σAmt¯t<450FB

=√0.1462+0.0472+0.0052+0.0402

(29)

σAmt¯t>450FB

=√0.1012+0.0492+0.0052+0.0882

(30)

σσt¯tσt¯t,SM

=0.15

(31)

for the error estimates, and with

Amt¯t<450FBobs

=−0.116

(32)

Amt¯t>450FBobs

=0.475

(33)

σt¯t,SM

=6.27

(34)

for the central values. The central values for AFB are the parton level values from Aaltonen:2011kc and the SM values for the cross-section are taken from our simulations of 5 million events.
The first two contributions to the AFB errors are from experiment, the third for the typical statistical error from our finite-sized simulated data samples, and the last is to account for possible NLO corrections: we take this contribution to be of the same size as the NLO SM asymmetry. These error estimates should be taken as rules of thumb to guide the eye in our figures for comparing SM against NP, rather than as hard and fast quantitative error budgets.

Figure 20: Scatter plots depicting simulated parton level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t} at Tevatron CM energy for t-channel flavor-changing scalar models listed in Table 3. The models are labeled by the mass of the mediator, the coupling to right-handed quarks, and the total Tevatron production cross-section. The cross-sections are compared against the SM cross-section which yields 6.3 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color. Figure 21: Scatter plots depicting simulated parton level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t} at Tevatron CM energy for t-channel flavor-changing vector models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total Tevatron production cross-section. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section which yields 6.3 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color. Figure 22: Scatter plots depicting simulated parton level {AFB(mt¯t<450GeV),AFB(mt¯t>450GeV),σt¯t} at Tevatron CM energy for axigluon models listed in Table 3. The models are labeled by the mass of the mediator, the coupling, and the total Tevatron production cross-section. The coupling conventions are discussed in detail in the text. The cross-sections are compared against the SM cross-section which yields 6.3 pb at the LO; the color scales for the models indicate the deviation from the SM cross-section, as indicated by the legend at the bottom. The curves indicate constant χ2 for a given cross-section, as defined in Eq. (22). Contours for four cross-section values (cyan, blue, green, purple) are shown for χ2/d.o.f.= 1 and 2. A single (cyan) χ2/d.o.f.=3 contour with SM cross-section is shown. Model points of a given color should be compared to χ2 contours of the same color.

Appendix B Event Generation

In this appendix, we describe our event generation setup and
strategies for data analysis presented in the main text of this
paper.
We employ FeynRules v1.4.10 for model file generationfeynrules ,
MadGraph5 1.3.3 for event generationAlwall:2011uj ,
PYTHIA v6
for parton showering and hadronizationSjostrand:2000wi , and a modified PGS4
for fast detector simulationPGS4 .

This work involves a large survey of different
models and model parameters, and model-dependent acceptance in
detection is an important issue in interpreting experimental observations.
Thus fast detector simulation on a large number of events is necessary.
Although there are criticisms on the credibility of fast detector
simulation tools, fast detector simulation tools like PGS4 are
indispensible for this paper.

To obtain more realistic and reliable results, we tune
the detector simulation and our analysis to the
current experiments in such a way that performance is not harmed.
For comparison of our results to data, we show NP models compared to
the SM with the same analysis setup. Then we can draw
conclusions on the status of NP models, since all experimental
analyses are accompanied with their own SM simulation.
In the following section, we summarize our considerations.

b.1 Fast Detector Simulation and Object Reconstruction

We simulate our model points given the specifications of the CDF detector at the Tevatron and from the ATLAS detector at the
LHC. We use the default detector parameters for CDF and ATLAS given
in the official distribution of PGS4. Some important detector
parameters used in PGS4 are summarized in Table 6.